Related papers: Generalized Transforms and Special Functions
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
This paper introduces a new method for redefining the Roman factorial using universally applicable functions that are not expressed in closed form. We present a set of foundational functions, similar to Boolean operations, to simplify the…
In this paper, we present the general one-dimensional Clifford Fourier Transform. We derive fundamental properties: Plancherel theorem, reconstruction and convolution formulas. Additionally, we provide an application to probability theory…
This paper refers to the study of generalized Struve type function. Using generalized Galue type Struve function (GTSF) by Nisar et al. [13], we derive various integral transform, including Euler transform, Laplace transform, Whittakar…
We survey and investigate some computational aspects of the Fourier-Mukai transform.
For any finite group $G$, we give an arithmetic algorithm to compute generalized Discrete Fourier Transforms (DFTs) with respect to $G$, using $O(|G|^{\omega/2 + \epsilon})$ operations, for any $\epsilon > 0$. Here, $\omega$ is the exponent…
In this paper, we aim at characterizing generalized functionals of discrete-time normal martingales. Let $M=(M_n)_{n\in \mathbb{N}}$ be a discrete-time normal martingale that has the chaotic representation property. We first construct…
It is shown that the Bellman function method can be applied to study the $L^p$-norms of general operators on martingales, i.e., of operators that are not necessarily martingale transforms. Informally, we provide a single Bellman-type…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
The present article deals with properties of one class of functions with complicated local structure. These functions can be modeled by certain operators of digits. Such operators were considered by the author earlier (for example, see [27,…
We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is…
In this paper, we introduced the theory of the sieve function transformation. Using the principle of sieve function transformation, we improved sieve method, and obtained the difference range of similar sieve function values. For this, we…
Although the vectorization operation is known and well-defined, it is only defined for 2-D matrices, and its inverse isn't as well-popularized. This work proposes to generalize the vectorization to higher dimensions, and define…
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and…
We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair…
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
Domain generalization aims to train models on multiple source domains so that they can generalize well to unseen target domains. Among many domain generalization methods, Fourier-transform-based domain generalization methods have gained…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…